Abstract
Buckling of axially compressed cylinders is a classic problem in engineering mechanics. Even though an analytical solution based on a linear eigenvalue analysis has existed for over 100 years, the buckling of cylinders continues to attract attention from researchers. This interest stems from the unstable nature of the buckling event with its associated severe sensitivity to initial imperfections—geometric, loading, boundary conditions, or otherwise—that rapidly erode the analytical or numerical predictions based on the perfect problem. A classical analysis of the compressed cylinder based on a linear eigenvalue analysis also suggests a periodic nature of the buckling modes, whereas highspeed photography experiments indicate that buckling is governed by the formation of one or multiple dimples that then multiply to cover the whole cylinder surface. Asymptotic expansions around the critical point, and branchswitching techniques based on extended arclength methods, show that the periodic buckling modes branching from the prebuckling path do indeed localise immediately after the bifurcation into solutions featuring one or multiple dimples. Tracing these dimple solutions in a pathfollowing solver with respect to applied compression demonstrates a sequential pattern formation whereby isolated dimples multiply circumferentially through a series of de and restabilisations. Furthermore, the singledimple solution forms an unstable equilibrium path, almost coincident with the prebuckling path, that corresponds to the smallest energy barrier between the prebuckling and postbuckling regimes. The small energy barrier associated with the singledimple solution means that the compressed, prebuckled cylinder is exceedingly sensitive to perturbations once the level of compression is exceeded for which the single dimple exists as an unstable equilibrium. It is possible to parametrise the compressive onset of the singledimple solution using a single nondimensional parameter, and the ensuing relation forms an alternative lowerbound design curve that shows good correlation with experimental results in the literature and other lowerbound curves suggested recently. The fact that localisations can form as unstable equilibrium solutions anywhere across the domain of the cylinder implies a large set of possible trajectories to instability, with each trajectory affine to a particular imperfection signature. This multiplicity of possible routes to buckling leads to a large spread in buckling loads even for seemingly indistinguishable random imperfections of equal amplitude. It is shown that the ability to control the equilibrium trajectory to buckling via dominant imperfections, or elastic tailoring using towsteered composites, creates interesting possibilities for designing imperfectioninsensitive shells.
Original language  English 

Publication status  Published  2020 
Event  23rd International Conference on Composite Structures & Mechanics of Composites 6  Online Duration: 1 Sep 2020 → 4 Sep 2020 https://events.unibo.it/iccs23/plenarylectures 
Conference
Conference  23rd International Conference on Composite Structures & Mechanics of Composites 6 

Period  1/09/20 → 4/09/20 
Internet address 
Bibliographical note
Invited plenary lectureFingerprint
Dive into the research topics of 'Localisation in buckling and postbuckling of cylindrical shells'. Together they form a unique fingerprint.Prizes

Royal Academy of Engineering Research Fellow
Groh, Rainer (Recipient), 2018
Prize: Prizes, Medals, Awards and Grants